2. FOUNDATIONS

There is now a substantial body of observations that support directly and indirectly the relativistic hot Big Bang model for the expanding Universe. Equally important, there are no data that are inconsistent. This is no mean feat: The observations are sufficiently constraining that there is no alternative to the hot Big Bang consistent with all the data at hand. Reports in the popular press of the death of the Big Bang usually confuse detailed aspects of the theory that are still in a state of flux, such as models of dark matter or scenarios for large-scale structure formation, with the basic framework itself. There are indeed many open problems in cosmology, such as the the age, size, and curvature of the Universe, the nature of the dark matter, and details of how large-scale structures form and how galaxies evolve - these issues are being addressed by a number of current observations. But the evidence that our Universe expanded from a dense hot phase roughly 13 billion years ago is now incontrovertible (see, e.g., Peebles et al. 1991).

When studied with modern optical telescopes, the sky is dominated by distant faint blue galaxies. To 30th magnitude per square arcsecond surface brightness (4 x 10^-18 erg sec^-1 cm^-2 arcsec^-2 in 100 nm bandwidth at 450 nm wavelength, or about five photons per minute per galaxy collected with a 4-meter mirror) there are about 50 billion galaxies over the sky. On scales less than around 100 Mpc galaxies are not distributed uniformly, but rather cluster in a hierarchical fashion. The correlation length for bright galaxies is 8h^-1 Mpc (at this distance from a galaxy the probability of finding another galaxy is twice the average). (1 Mpc = 3.09 x 10²⁴ cm 3 million light years, and h = H₀ / 100 km s^-1 Mpc^-1 is the dimensionless Hubble constant.)

About 10 percent of galaxies are found in clusters of galaxies, the largest of which contain thousands of galaxies. Like galaxies, clusters are gravitationally bound and no longer expanding. Fritz Zwicky was among the first to study clusters, and George Abell created the first systematic catalogue of clusters of galaxies in 1958; since then, some four thousand clusters have been identified (most discovered by optical images, but a significant number by the x-rays emitted by the hot intracluster gas). Larger entities called superclusters, are just now ceasing to expand and consist of several clusters. Our own supercluster was first identified in 1937 by Holmberg, and characterized by de Vaucouleurs in 1953. Other features in the distribution of galaxies in 3-dimensional space have also been identified: regions devoid of bright galaxies of size roughly 30 h^-1 Mpc (simply called voids) and great walls of galaxies which stretch across a substantial fraction of the sky and appear to be separated by about 100 h^-1 Mpc. Figure 1 is a three panel summary of our knowledge of the large-scale structure of the Universe.

Figure 1. Large-scale structure in the Universe as traced by bright galaxies: (upper left) The Great Wall, identified by Geller and Huchra (1989) [updated by E. Falco]. This coherent object stretches across most of the sky; walls of galaxies are the largest known structures (see Oort 1983). We are at the apex of the wedge, galaxies are placed at their ``Hubble distances'', d = H0-1 Mu; note too, the ``voids'' relatively devoid of galaxies. (upper right) Pie-diagram from the Las Campanas Redshift Survey (Shectman et al. 1996). Note the structure on smaller length scales including voids and walls, which on larger scales dissolves into homogeneity. (lower) Redshift-histogram from deep pencil-beam surveys (Willmer et al. 1994; Broadhurst et al. 1990) [updated by T. Broadhurst.] Each pencil beam covers only a square degree on the sky. The narrow width of the beam ``distorts'' the view of the Universe, making it appear more inhomogeneous. The large spikes spaced by around 100 h-1 Mpc are believed to be great walls.

The factor H₀, now called the Hubble constant, is the expansion rate at the present epoch. Hubble's measurements of H₀ began at 550 km s^-1 Mpc^-1; a number of systematic errors were identified, and by the 1960s H₀ had dropped to 100 km s^-1 Mpc^-1. Over the last two decades controversy surrounded H₀, with measurements clustered around 50 km s^-1 Mpc^-1 and 90 km s^-1 Mpc^-1. In the past two years or so, much progress has been made because of the calibration of standard candles by the Hubble Space Telescope (see e.g., Filippenko and Riess 1998; Madore et al. 1998), and there is now a general consensus that H₀ = (67 ± 10) km s^-1 Mpc^-1 (where ± 10 km s^-1 Mpc^-1 includes both statistical and systematic error; see Fig. 2). The inverse of the Hubble constant - the Hubble time - sets a timescale for the age of the Universe: H₀^-1 = (15 ± 2) Gyr.

Figure 2. Hubble diagram based upon distances to supernovae of type 1a (SNe1a). Note the linearity; the slope, or Hubble constant, H0 = 64 km s-1 Mpc-1 (Courtesy, A. Riess; see Filippenko & Riess 1998).

By now, through observations of a variety of phenomena from optical galaxies to radio galaxies, the cosmological interpretation of redshift is very well established. Two recent interesting observations provide further evidence: numerous examples of high-redshift objects being gravitationally lensed by low redshift objects near the line of sight; and the fading of supernovae of type Ia, whose light curves are powered by the radioactive decay of Ni⁵⁶, at high redshift exhibiting time dilation by the predicted factor of 1 + z (Leibundgut et al. 1996).

Figure 3. Contours of constant time back to the big bang in the M - plane. The three bold solid lines are for h = 0.65; the light solid lines are for h = 0.7; and the dotted lines are for h = 0.6. The diagonal line corresponds to a flat Universe. Note, for h ~ 0.65 and t0 ~ 13 Gyr a flat Universe is possible only if ~ 0.6; M = 1 is only possible if t0 ~ 10 Gyr and h ~ 0.6.

An important consistency test of the standard cosmology is the congruence of the Hubble time with other independent determinations of the age of the Universe. (The product of the Hubble constant and the time back to the big bang, H₀ t₀, is expected to be between 2/3 and 1, depending upon the density of matter in the Universe; see Fig. 3.) Since the discovery of the expansion, there have been occasions when the product H₀t₀ far exceeded unity, indicating an inconsistency. Both H₀ and t₀ measurements have been plagued by systematic errors. Slowly, the situation has improved, and at present there is consistency within the uncertainties. Chaboyer et al. (1998) date the oldest globular stars at 11.5 ± 1.3 Gyr; to obtain an estimate of the age of the Universe, another 1-2 Gyr must be added to account for the time to the formation of the oldest globular clusters. Age estimates based upon abundance ratios of radioactive isotopes produced in stellar explosions, while dependent upon the time history of heavy-element nucleosynthesis in our galaxy, provide a lower limit to the age of the Galaxy of 10 Gyr (Cowan et al. 1991). Likewise, the age of the Galactic disk based upon the cooling of white dwarfs, > 9.5 Gyr, is also consistent with the globular cluster age (Oswalt et al. 1996). Recent type Ia supernova data yield an expansion age for the Universe of 14.0 ± 1.5 Gyr, including an estimate of systematic errors (Riess et al. 1998).

Within the uncertainties, it is still possible that H₀t₀ is slightly greater than one. This could either indicate a fundamental inconsistency or the presence of a cosmological constant (or something similar). A cosmological constant can lead to accelerated expansion and H₀t₀ > 1. Recent measurements of the deceleration of the Universe, based upon the distances of high-redshift supernovae of type Ia (SNe1a), in fact show evidence for accelerated expansion; we will return to these interesting measurements later.

Figure 4. Spectrum of the Cosmic Microwave Background Radiation as measured by the FIRAS instrument on COBE and a black body curve for T = 2.7277 K. Note, the error flags have been enlarged by a factor of 400. Any distortions from the Planck curve are less than 0.005% (see Fixsen et al. 1996).

Another observational pillar of the Big Bang is the 2.73 K cosmic microwave background radiation [CMB] (see Wilkinson 1999). The FIRAS instrument on the Cosmic Background Explorer [COBE] satellite has probed the CMB to extraordinary precision (Mather et al. 1990). The observed CMB spectrum is exquisitely Planckian: any deviations are smaller than 300 parts per million (Fixsen et al. 1996), and the temperature is 2.7277 ± 0.002 K (see Fig. 4). The only viable explanation for such perfect black-body radiation is the hot, dense conditions that are predicted to exist at early times in the hot Big Bang model. The CMB photons last scattered (with free electrons) when the Universe had cooled to a temperature of around 3000 K (around 300,000 years after the Big Bang), and ions and electrons combined to form neutral atoms. Since then the temperature decreased as 1 + z, with the expansion preserving the black body spectrum. The cosmological redshifting of the CMB temperature was confirmed by a measurement of a temperature of 7.4 ± 0.8 K at redshift 1.776 (Songaila et al. 1994) and of 7.9± 1 K at redshift 1.973 (Ge et al. 1997), based upon the population of hyperfine states in neutral carbon atoms bathed by the CMB.

The CMB is a snapshot of the Universe at 300,000 yrs. From the time of its discovery, its uniformity across the sky (isotropy) was scrutinized. The first anisotropy discovered was dipolar with an amplitude of about 3 mK, whose simplest interpretation is a velocity with respect to the cosmic rest frame. The FIRAS instrument on COBE has refined this measurement to high precision: the barycenter of the solar system moves at a velocity of 370 ± 0.5 km s^-1. Taking into account our motion around the center of the Galaxy, this translates to a motion of 620 ± 20 km s^-1 for our local group of galaxies. After almost thirty years of searching, firm evidence for primary anisotropy in the CMB, at the level of 30 µK (or T/T 10^-5) on angular scales of 10° was found by the DMR instrument on COBE (see Fig. 5). The importance of this discovery was two-fold. First, this is direct evidence that the Universe at early times was extremely smooth since density variations manifest themselves as temperature variations of the same magnitude. Second, the implied variations in the density were of the correct size to account for the structure that exists in the Universe today: According to the standard cosmology the structure seen today grew from small density inhomogeneities ( / ~ 10^-5) amplified by the attractive action of gravity over the past 13 Gyr.

Figure 5. Summary of current measurements of the power spectrum of CMB temperature variations across the sky against spherical harmonic number l for several experiments. The first acoustic peak is evident. The light curve, which is preferred by the data, is a flat Universe (0 = 1, M = 0.35), and the dark curve is for a open Universe (0 = 0.3) [courtesy of M. Tegmark].

The final current observational pillar of the standard cosmology is big-bang nucleosynthesis [BBN]. When the Universe was seconds old and the temperature was around 1 MeV a sequence of nuclear reactions led to the production of the light elements D, ³He, ⁴He and ⁷Li. In the 1940s and early 1950s, Gamow and his collaborators suggested that nuclear reactions in the early Universe could account for the entire periodic table; as it turns out Coulomb barriers and the lack of stable nuclei with mass 5 and 8 prevent further nucleosynthesis. In any case, BBN is a powerful and very early test of the standard cosmology: the abundance pattern of the light elements predicted by BBN (see Fig. 6) is consistent with that seen in the most primitive samples of the cosmos. The abundance of deuterium is very sensitive to the density of baryons, and recent measurements of the deuterium abundance in clouds of hydrogen at high redshift (Burles & Tytler 1998a, b) have pinned down the baryon density to a precision of 10%.

Figure 6. Predicted abundances of 4He (mass fraction), D, 3He, and 7Li (relative to hydrogen) as a function of the baryon density. The broader band denotes the concordance interval based upon all four light elements. The narrower, darker band highlights the determination of the baryon density based upon a measurement of the primordial abundance of the most sensitive of these - deuterium (Burles & Tytler 1998a, b), which implies Bh2 = 0.02 ± 0.002.

As Schramm emphasized, BBN is also a powerful probe of fundamental physics. In 1977 he and his colleagues used BBN to place a limit to the number of neutrino species (Steigman et al. 1977), N < 7, which, at the time, was very poorly constrained by laboratory experiments, N less than a few thousand. The limit is based upon the fact that the big-bang ⁴He yield increases with N; see Fig. 7). In 1989, experiments done at e^± colliders at CERN and SLAC determined that N was equal to three, confirming the cosmological bound, which then stood at N < 4. Schramm used the BBN limit on N to pique the interest of many particle physicists in cosmology, both as a heavenly laboratory and in its own right. This important cosmological constraint, and many others that followed, helped to establish the ``inner space - outer space connection'' that is now flourishing.

Figure 7. The dependence of primordial 4He production, relative to hydrogen, YP, on the number of light neutrino species. The vertical band denotes the baryon density inferred from the Burles - Tytler measurement of the primordial deuterium abundance (Burles & Tytler 1998a, b); using YP < 0.25, based upon current 4He measurements, the BBN limit stands at N < 3.4 (from Schramm and Turner 1998).